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A vector of magnitude 10 along the nor...

A vector of magnitude 10 along the normal to the curve `3x^2+8x y+2y^2-3=0` at its point `P(1,0)` can be (a).`6 hat i+8 hat j` (b). `-8 hat i+3 hat j` (c). `6 hat i-8 hat j` (d). `8 hat i+6 hat j`

A

`6hati + 8hatj`

B

`-8 hati + 3hatj`

C

`6hati - 8 hatj`

D

`8 hati + 6 hatj`

Text Solution

Verified by Experts

The correct Answer is:
a
Differentiate the curve
`6x + 8 ( xy_(1) + y) + 4 yy_(1) =0`
`m_(T)at (1,0) is 6 + 8 (y_(1)(0)) =0`
` y_(1) (0) = -3/4`
`m_(N)= 4/3`
Unit vector =` +- (3hati + 4hatj) / 5`
Again normal of magnitude ` 10 =+- (6hati + 8hatj)`
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CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. If (vecaxxvecb)xx(vecbxxvecc)=vecb, where veca,vecb and vecc are non z...

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  2. If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and...

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  3. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y^...

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  4. If veca and vecb are two unit vectors inclined at an angle pi/3 then {...

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  5. If veca and vecb are othogonal unit vectors, then for a vector vecr no...

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  6. If veca+vecb ,vecc are any three non- coplanar vectors then the equa...

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  7. Sholve the simultasneous vector equations for vecx and vecy: vecx+vecc...

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  8. The condition for equations vecrxxveca = vecb and vecr xx vecc = vecd ...

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  9. If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2h...

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  10. If veca=2hati + hatj+ hatk, vecb= hati+ 2hatj + 2hatk,vecc = hati+ hat...

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  11. Let (veca (x) = (sin x) hati+ (cos x) hatj and vecb(x) = (cos 2x) hati...

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  12. For any vectors veca and vecb, (veca xx hati) + (vecb xx hati) + ( vec...

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  13. If veca,vecb and vecc are three non coplanar vectors and vecr is any v...

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  14. If vecP = (vecbxxvecc)/([vecavecbvecc]).vecq=(veccxxveca)/([veca vecb ...

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  15. A (veca), B (vecb) and C (vecc) are the vertices of triangle ABC and R...

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  16. If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is ...

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  17. If V be the volume of a tetrahedron and V ' be the volume of another...

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  18. [(veca xxvecb)xx(vecb xx vecc) (vecb xxvecc) xx (vecc xxveca)...

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  19. If vecr=x(1)(vecaxx vecb) + x(2) (vecb xxveca) + x(3)(vecc xxvecd) and...

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  20. If veca bot vecb then vector vecv in terms of veca and vecb satisfying...

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